## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |

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Resultat 1-5 av 100

Side 4

vitiated ; for instance , by substituting a shorter , but insufficient

the 18th Prop . of the 5th Book , in place ... Now this Proposition is a Theorem ,

not a Definition ; because the equality of figures of any kind must be

vitiated ; for instance , by substituting a shorter , but insufficient

**Demonstration**ofthe 18th Prop . of the 5th Book , in place ... Now this Proposition is a Theorem ,

not a Definition ; because the equality of figures of any kind must be

**demonstrated**... Side 5

... nor of this case is there any

though it is quite necessary there should be one . ... and all these Propositions

have , for these reasons , been insufficiently

hitherto .

... nor of this case is there any

**Demonstration**in the Elements we now have ,though it is quite necessary there should be one . ... and all these Propositions

have , for these reasons , been insufficiently

**demonstrated**since Theon's timehitherto .

Side 15

Which was to be

isosceles triangle are equal to one another : and , if the equal sides be produced

, the angles upon the other side of the base shall be equal . Let ABC be ...

Which was to be

**demonstrated**. PROP . V. THEOR . Tue angles at the base of anisosceles triangle are equal to one another : and , if the equal sides be produced

, the angles upon the other side of the base shall be equal . Let ABC be ...

Side 16

and their remaining angles , each to each , to which the equal sides are opposite

; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the

angle CBG ; and , since it has been

and their remaining angles , each to each , to which the equal sides are opposite

; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the

angle CBG ; and , since it has been

**demonstrated**, that the whole angle ABG is ... Side 20

By help of this problem , it may be

have a common segment . If it be possible , let the two straight lines ABC , ABD

have the segment AB common to both of them . From the point B draw BE at right

...

By help of this problem , it may be

**demonstrated**, that two straight lines cannothave a common segment . If it be possible , let the two straight lines ABC , ABD

have the segment AB common to both of them . From the point B draw BE at right

...

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The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base BC is given centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole